pyefd 1.0

Python implementation of "Elliptic Fourier Features of a Closed Contour"

PyEFD

An Python/NumPy implementation of a method for approximating a contour with a Fourier series, as described in [1].

Installation

$ pip install pyefd

Usage

Given a closed contour of a shape, generated by e.g. scikit-image or OpenCV, this package can fit a Fourier series approximating the shape of the contour:

from pyefd import elliptic_fourier_descriptors
coeffs = elliptic_fourier_descriptors(contour, order=10)

The coefficients returned are the a_n, b_n, c_n and d_n of the following Fourier series representation of the shape.

The coefficients returned are by default normalized so that they are rotation and size-invariant. This can be overridden by calling:

from pyefd import elliptic_fourier_descriptors
coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=False)

Normalization can also be done afterwards:

from pyefd import normalize_efd
coeffs = normalize_efd(coeffs)

To use these as features, one can write a small wrapper function:

def efd_feature(contour):
    coeffs = elliptic_fourier_descriptors(contour, order=10, normalize=True)
    return coeffs.flatten()[3:]

If the coefficients are normalized, then coeffs[0, 0] = 1.0, coeffs[0, 1] = 0.0 and coeffs[0, 2] = 0.0, so they can be disregarded when using the elliptic Fourier descriptors as features.

See [1] for more technical details.

Testing

Run tests with:

$ python setup.py test

or with Pytest:

$ py.test tests.py

The tests includes a single image from the MNIST dataset of handwritten digits ([2]) as a contour to use for testing.

Documentation

See ReadTheDocs.

References

[1] (1,2)

Frank P Kuhl, Charles R Giardina, Elliptic Fourier features of a closed contour, Computer Graphics and Image Processing, Volume 18, Issue 3, 1982, Pages 236-258, ISSN 0146-664X, http://dx.doi.org/10.1016/0146-664X(82)90034-X.

[2]

LeCun et al. (1999): The MNIST Dataset Of Handwritten Digits

v1.0 (2016-04-19)

• Deemed stable enough for version 1.0 release

• Created documentation.

v0.1.2 (2016-02-29)

• Testing with pytest instead of nosetests.

• Added Coveralls use.

v0.1.1 (2016-02-17)

• Fixed MANIFEST

• Added LICENSE file that was missing.

v0.1.0 (2016-02-09)

• Initial release